Lowering Inventory Systems Costs by Using Regression-Derived Estimators of Demand Variability*

Scientific techniques for inventory management typically are applied to systems containing many items. Such techniques require an estimation of the demand variance (and mean) of each item from historical data. This research demonstrates a significant potential for improvement in system cost performance from using least-squares regression fits of a variance-to-mean functional relation instead of the standard statistical variance estimate. Even when there is a moderate degree of heterogeneity among items and when the form of the variance-to-mean relation is misspecified, substantial cost savings may be realized. The cost of statistical uncertainty may be reduced by half. The research also provides evidence that system cost is fairly insensitive to the number of items used to fit the regression. This paper provides the underlying reason why a regression-derived variance estimator yields lower cost: it is less variable than the usual individual item variance estimator.     

Integrating Analysis and Communication Skills into the Decision Science Curriculum*

The teaching of decision sciences presupposes that careful attention is directed toward improving students' critical thinking and analytical skills. This paper presents an approach to teaching quantitative methods classes that focuses on developing student skills in the areas of analytical and critical thinking through written and oral communication. The approach requires very little additional instructor preparation time and does not require the instructor to make major changes in either the content or organization of the course. While the instructor's investment is minimal, the benefits to the students appear to be substantial.     

A Bayesian Approach for Analyzing Results of Vehicle Collision Tests

Certain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.     

Characterization of Unacceptable Solutions in LP Discriminant Analysis*

Many linear programming models have been proposed for performing discriminant analysis. Partial characterizations for unacceptable solutions have been presented and new models proposed to circumvent these problems. In this paper those conditions leading to unacceptable solutions for all two-group models are characterized.     

Inference in a Binary Response Model with Applications to Data Analysis*

Standard errors of the coefficients of a logistic regression (a binary response model) based on the asymptotic formula are compared to those obtained from the bootstrap through Monte Carlo simulations. The computer intensive bootstrap method, a nonparametric alternative to the asymptotic estimate, overestimates the true value of the standard errors while the asymptotic formula underestimates it. However, for small samples the bootstrap estimates are substantially closer to the true value than their counterpart derived from the asymptotic formula. The methodology is discussed using two illustrative data sets. The first example deals with a logistic model explaining the log-odds of passing the ERA amendment by the 1982 deadline as a function of percent of women legislators and the percent vote for Reagan. In the second example, the probability that an ingot is ready to roll is modelled using heating time and soaking time as explanatory variables. The results agree with those obtained from the simulations. The value of the study to better decision making through accurate statistical inference is discussed.     

A NEW CLASS OF MODELS FOR THE DISCRIMINANT PROBLEM

Discriminant analysis is relevant to business decision making in a variety of contexts, such as when one decides to make or buy a specified component, fund a venture project, or hire a particular person. Potential applications in artificial intelligence, particularly in the area of pattern recognition, have further underscored the importance of the field. A recent innovation in discriminant analysis is provided by special linear programming (LP) models, which offer attractive alternatives to classical statistical approaches. The scope of application in which discriminant analysis can be advantageously employed is broadened by the flexibility to tailor parameters in the LP approaches to reflect diverse goals and by the power to explore the sensitivity of these parameters. In spite of the promise of the LP formulations, however, limitations to their effectiveness have been uncovered in certain settings. A recent advance involving a normalization construct removes some of the limitations but entails solving the LP model twice (to allow for different signs of a normalization constant) and does not yield equivalent solutions for different rotations of the problem data. This paper introduces a new model and a new class of normalizations that remedy both remaining limitations, making it possible to take advantage of the modeling capabilities of the LP formulations without the attendant shortcomings encountered by earlier investigations. Our development shows by empirical testing and illustrative analysis that the quality of solutions from LP discriminant approaches is more favorable (relative to the classical model) than previously supposed.     

INSTRUCTING OPERATIONS DESIGN: AN EXPERIENTIAL APPROACH

Teaching an operations design course has major pedagogical challenges. (1) The design topics—output, process, facility, and work design—are necessarily taught sequentially, yet the decisions are integrative. (2) Instruction must be generic to service or product producers. (3) Discussing output design is difficult since students typically have had no exposure to the “product language” of engineering graphics. (4) No text is available which examines in sufficient depth all the operations design decisions. (5) Cases necessarily depict historical situations—process technologies and economic data—while operations managers must plan future directions for their productive systems. (6) While the commercial world contains fresh information and data, students are inexperienced in obtaining knowledge from the real world. (7) While the course presents an operations management perspective, students must recognize the information, data, and cooperation necessary from the other functional areas to successfully complete the operations design. To help overcome these seven pedagogical challenges, the students in the undergraduate and graduate operation design courses complete a comprehensive feasibility study for a new product or service and the entire productive system.     

A Variable Selection Criterion in the Linear Programming Approaches to Discriminant Analysis*

There are numerous variable selection rules in classical discriminant analysis. These rules enable a researcher to distinguish significant variables from nonsignificant ones and thus provide a parsimonious classification model based solely on significant variables. Prominent among such rules are the forward and backward stepwise variable selection criteria employed in statistical software packages such as Statistical Package for the Social Sciences and BMDP Statistical Software. No such criterion currently exists for linear programming (LP) approaches to discriminant analysis. In this paper, a criterion is developed to distinguish significant from nonsignificant variables for use in LP models. This criterion is based on the “jackknife” methodology. Examples are presented to illustrate implementation of the proposed criterion.     

Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

The adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.     

Monotonic change point estimation of generalized linear model-based regression profiles

In this article, a maximum likelihood estimator is derived in the generalized linear model-based regression profiles under monotonic change in Phase II. The performance of the proposed estimator is comprehensively investigated through some special cases, and compared with estimators under step change and drift. The results show that the proposed estimator has better performance in small and medium shifts under different increasing changes. Finally, the applicability of the proposed estimator is illustrated using a real case.